Question: Solve for $x$ and $y$ using elimination. ${2x-3y = -14}$ ${-6x-4y = -62}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $3$ ${6x-9y = -42}$ $-6x-4y = -62$ Add the top and bottom equations together. $-13y = -104$ $\dfrac{-13y}{{-13}} = \dfrac{-104}{{-13}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {2x-3y = -14}\thinspace$ to find $x$ ${2x - 3}{(8)}{= -14}$ $2x-24 = -14$ $2x-24{+24} = -14{+24}$ $2x = 10$ $\dfrac{2x}{{2}} = \dfrac{10}{{2}}$ ${x = 5}$ You can also plug ${y = 8}$ into $\thinspace {-6x-4y = -62}\thinspace$ and get the same answer for $x$ : ${-6x - 4}{(8)}{= -62}$ ${x = 5}$